Piotr Achinger Title: Etale homotopy and wild ramification Abstract: I will start with a gentle introduction to the etale homotopy theory, which is tool invented by Artin, Grothendieck and Mazur in the 1960s which permits one to employ the methods of algebraic topology to study algebraic varieties defined over fields other than the complex numbers. A particular emphasis will be put on the fundamental group and the use of coverings by K(pi, 1) spaces. In the second part of the talk I will discuss problems in etale homotopy arising in positive characteristic, most of them tightly related to wild ramification phenomena. Basing on the very recent progress towards the understanding of wild ramification through the characteristic cycle (a notion inspired by the classical theory of D-modules) due to Beilinson, Deligne, and T. Saito, I proved that every affine scheme in positive characteristic (as well as every affinoid p-adic analytic space) is a K(pi, 1) space for the etale topology. I will sketch the proof of this result.